Problem: Multiply the following complex numbers: $({5-5i}) \cdot ({-4+i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({5-5i}) \cdot ({-4+i}) = $ $ ({5} \cdot {-4}) + ({5} \cdot {1}i) + ({-5}i \cdot {-4}) + ({-5}i \cdot {1}i) $ Then simplify the terms: $ (-20) + (5i) + (20i) + (-5 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -20 + (5 + 20)i - 5i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -20 + (5 + 20)i - (-5) $ The result is simplified: $ (-20 + 5) + (25i) = -15+25i $